From a point p on level ground, the angle of elevation of the top of a tree is 60 degrees. if the tree is 39 m high, how far is its base from p
22.5m(39/3^2m)
I need a solution that will match the answer (22.5m )
39/x=tan60°
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22.5m
To find the distance between the base of the tree and point P, we can make use of trigonometry.
Let's denote the distance between the base of the tree and point P as x.
From point P, we have an angle of elevation of 60 degrees to the top of the tree. This means that we have a right-angled triangle formed between point P, the top of the tree, and the base of the tree.
In this triangle, the height of the tree (opposite side) is given as 39 meters, and we need to find the base of the tree (adjacent side), which is the same as finding the value of x.
Using trigonometry, we can use the tangent function to relate the angle and sides of the triangle:
tan(angle) = Opposite/Adjacent
So, we have:
tan(60 degrees) = 39 meters / x
To solve for x, we can rearrange the equation:
x = 39 meters / tan(60 degrees)
Calculating this using a calculator:
x ≈ 39 meters / 1.732 (rounded to three decimal places)
x ≈ 22.49 meters
Therefore, the base of the tree is approximately 22.49 meters away from point P.